I kind of feel like this was JKR giving an explanation for all those people who would say "well why couldn't Harry just use a time-turner??" But although I see what you mean with Snape, I feel like that can be explained as it was an alternative universe. Draco on the other hand...I'm not too sure. Perhaps the changes could be explained by his love for his son (and I s'pose, wife as well.) I agree about Delphi, it just didn't feel right. In fact, I kind of feel like the whole thing was a bit rushed. I know that's probably because it's a play and the entire plot did have to be fit into a certain time period, but reading it, I think maybe as a book, the plot and characters just needed fleshing out a bit more.
Something that I was really disappointed by was Ron, however. In the original books, he was such a good character - strong, funny, a good friend etc. But the play seemed to only use him as comic relief. It was as if he had no purpose other than to eat and make the audience laugh. I felt that the Golden Trio was more like the Golden Quartet, with Ginny and Draco replacing Ron. They almost turned him into the Ron Weasley the films had portrayed, which didn't really do him justice.
However, I loved the characters of Scorpius and Albus. I think their relationship was great - it was funny and heartwarming and I liked how both of them were trying to work things out away from their fathers and the celebrity that came with being their sons. I kind of wish their friendship was featured more, like the earlier years, because they were skipped and I bet the two had some pretty fun escapades.
I know for certain that I am not reading this so I went ahead and read the spoilers here just to know what this is all about.